DATE values are numeric. So use a numeric missing value, not a character string. Or use the CALL MISSING() function.
data Work.Quest_Results_3;
set Work.Quest_Results_2;
term1 = input(terminationdate, mmddyy10.);
termed = term1;
if termed > '01SEP2022'd then call missing(termed);
format term1 termed YYMMDD10. ;
run;
Are you trying to do a censored survival analysis?
In that case it might be better to use a truncated date instead of setting the later dates to missing.
data Work.Quest_Results_3;
set Work.Quest_Results_2;
term1 = input(terminationdate, mmddyy10.);
censored = term1 > '01SEP2022'd ;
termed = min(term1,'01SEP2022'd);
format term1 termed YYMMDD10. ;
run;
PS Displaying dates in MDY or DMY order will confuse 50% of your audience. Display them using YMD order or the DATE format to avoid confusing May First for the Fifth of January.